Step 1: Pit the cherries if they haven’t been pitted already: you’ll need 1 1/2 cups.
Step 2: Start the sauce: Place the sugar and water in a small saucepan. Cover and bring to a boil. Uncover the pan and cook the sugar until darkly caramelized, 5 minutes, swirling the pan. Do not stir. Remove the pan from the heat and add the vinegar: the mixture will sputter and hiss like Mt. Vesuvius. Return the pan to the heat and simmer, whisking, until the caramel dissolves.
Step 3: Add the port wine, lemon zest, and lemon juice and bring to a boil over high heat. Stir in the stock, cinnamon, and chipotle. Reduce the heat and simmer until richly flavored, 5 minutes. Add the cherries and cook until soft but not mushy, 3 minutes for fresh, 1 minute for frozen. Remove and discard the cinnamon stick.
Step 4: Dissolve the cornstarch in the kirsch to make a paste. Whisk this mixture into the sauce and boil for 1 minute. The sauce will thicken slightly. Whisk in the butter and salt and pepper to taste: the sauce should be highly seasoned. If you like a sweeter sauce, add a little more sugar.
Serve with Cherry-Smoked Duck.